FORMULATION AND DIGITAL CODING OF APPROXIMATE HYDROGEN PROPERTIES FOR APPLICATION TO HEAT-TRANSFER AND FLUID-FLOW COMPUTATIONS
Heat and fluid flow computations - fortran digital computer
LIQUID FLOW↗
SEARCH · Search NASA
Results for “Approximate Computing”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Large-scale harmonic balance simulations with Krylov subspace and preconditioner recycling
The multi-harmonic balance method combined with numerical continuation provides an efficient framework to compute a family of time-periodic solutions, or response curves, for large-scale, nonlinear mechanical systems. The predictor and corrector steps repeatedly solve a sequence of linear systems that scale by the model size and number of harmonics in the assumed Fourier series approximation. In this paper, a novel Newton–Krylov iterative method is embedded within the multi-harmonic balance and continuation algorithm to efficiently compute the approximate solutions from the sequence of linear systems that arise during the prediction and correction steps. Further, the method recycles, or reuses, both the preconditioner and the Krylov subspace generated by previous linear systems in the solution sequence. A delayed frequency preconditioner refactorizes the preconditioner only when the performance of the iterative solver deteriorates. The GCRO-DR iterative solver recycles a subset of harmonic Ritz vectors to initialize the solution subspace for the next linear system in the sequence. The performance of the iterative solver is demonstrated on two exemplars with contact-type nonlinearities and benchmarked against a direct solver with traditional Newton–Raphson iterations.
97 MATHEMATICS AND COMPUTING↗
The frequencies of cantilever wings in beam and torsional vibrations
Methods are described for calculating the period and frequency of vibration of cantilever wings and similar structures in which the weight and moment of inertia vary along the span. Both the beam and torsional frequencies may be calculated by these methods. The procedure is illustrated by examples. It is shown that a surprisingly close approximation to the beam frequency may be obtained by a very brief calculation in which the curvature of the wing in vibration is assumed to be constant. A somewhat longer computation permits taking account of the true curvature of the beam by a series of successive approximations which are shown to be strongly convergent. Analogous methods are applied to calculations of the torsional frequency. For the first approximation it is assumed that the angle of twist varies linearly alone the semispan. True variation of the twist is computed by successive approximations which are strongly convergent, as in the case of beam vibrations.
Burgess, C P↗
Eccentric Form of the Loss of Stability of a Rotating Elastoplastic Radially Inhomogeneous Stepped Circular Disk
We propose a procedure for the investigation of the possible loss of stability of a rotating elastoplastic radially inhomogeneous stepped circular disk by the method of small parameter. The characteristic equation for the critical radius of the plastic zone is obtained in the first approximation. The values of the critical angular rotational velocity are numerically found for various parameters of the disk.
97 MATHEMATICS AND COMPUTING↗
Exact sum rules with approximate ground states
Electromagnetic and weak transitions tell us a great deal about the structure of atomic nuclei. Yet modeling transitions can be difficult: it is often easier to compute the ground state, if only as an approximation, than excited states. One alternative is through transition sum rules, in particular the non-energy-weighted and energy-weighted sum rules, which can be computed as expectation values of operators. We investigate by computing sum rules for a variety of nuclei, comparing the numerically exact full configuration-interaction shell model, as a reference, to Hartree-Fock, projected Hartree-Fock, and the nucleon pair approximation. Furthermore, these approximations yield reasonable agreement, which we explain by prior work on the systematics of transition moments.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
The growth of the tearing mode - Boundary and scaling effects
A numerical model of resistive magnetic tearing is developed in order to verify and relate the results of the principal approximations used in analytic analyses and to investigate the solutions and their growth-rate scalings over a large range of primary parameters which include parametric values applicable to the solar atmosphere. The computations cover the linear behavior for a variety of boundary conditions, emphasizing effects which differentiate magnetic tearing in astrophysical situations from that in laboratory devices. Eigenfunction profiles for long and short wavelengths are computed and the applicability of the 'constant psi' approximation is investigated. The growth rate is computed for values of the magnetic Reynolds number up to a trillion and of the dimensionless wavelength parameter down to 0.001. The analysis predicts significant effects due to differing values of the magnetic Reynolds number.
Steinolfson, R. S.↗
A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator
Our manuscript demonstrates a technique for efficiently solving the classical wave equation, the shallow water equations, and, more generally, equations of the form ∂u/∂t=Lu∂u/∂t=Lu, where LL is a skew-Hermitian differential operator. The idea is to explicitly construct an approximation to the time-evolution operator exp(τL)exp(τL) for a relatively large time-step ττ. Recently developed techniques for approximating oscillatory scalar functions by rational functions, and accelerated algorithms for computing functions of discretized differential operators are exploited. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many characteristic wavelengths and large speed-ups over existing methods in situations where simulation over long times are required. Numerical examples involving the 2D rotating shallow water equations and the 2D wave equation in an inhomogenous medium are presented, and the method is compared to the 4th order Runge–Kutta (RK4) method and to the use of Chebyshev polynomials. The new method achieved high accuracy over long-time intervals, and with speeds that are orders of magnitude faster than both RK4 and the use of Chebyshev polynomials.
97 MATHEMATICS AND COMPUTING↗
Applications of Analytic Models to Spent Fuel Cask Analysis
The advent of high performance computing has changed the way scientists and engineers solve problems. Scientists previously would make a tremendous effort to simplify a complex problem to it’s essence by reducing geometry, neglecting changes and only preserving first-order effects. Now, scientist are able to leave the details in the problem and computationally arrive at a result. To develop the computational physics programs used by scientists, developers make assumptions and use approximation to reduce complex, continuous calculus to algebraic expressions which computers are able to solve.
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Low rank approximation in simulations of quantum algorithms
Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits can be simulated efficiently on a classical computer if the input quantum state is a low rank tensor and all intermediate states of the quantum algorithm can be represented or approximated by low rank tensors. Here, in this paper, we examine the possibility of simulating a few quantum algorithms by using low-rank canonical polyadic (CP) decomposition to represent the input and all intermediate states of these algorithms. Two rank reduction algorithms are used to enable efficient simulation. We show that some of the algorithms preserve the low rank structure of the input state and can thus be efficiently simulated on a classical computer. However, the rank of the intermediate states in other quantum algorithms can increase rapidly, making efficient simulation more difficult. To some extent, such difficulty reflects the advantage or superiority of a quantum computer over a classical computer. As a result, understanding the low rank structure of a quantum algorithm allows us to identify algorithms that can benefit significantly from quantum computers.
97 MATHEMATICS AND COMPUTING↗
Data-driven quantum approximate optimization algorithm for power systems
Abstract Quantum technology provides a ground-breaking methodology to tackle challenging computational issues in power systems. It is especially promising for Distributed Energy Resources (DERs) dominant systems that have been widely developed to promote energy sustainability. In those systems, knowing the maximum sections of power and data delivery is essential for monitoring, operation, and control. However, high computational effort is required. By leveraging quantum resources, Quantum Approximate Optimization Algorithm (QAOA) provides a means to search for these sections efficiently. However, QAOA performance relies heavily on critical parameters, especially for weighted graphs. Here we present a data-driven QAOA, which transfers quasi-optimal parameters between weighted graphs based on the normalized graph density. We verify the strategy with 39,774 expectation value calculations. Without parameter optimization, our data-driven QAOA is comparable with the Goemans-Williamson algorithm. This work advances QAOA and pilots its practical application to power systems in noisy intermediate-scale quantum devices.
Jing, Hang (ORCID:0000000256343489)↗
Combining the ensemble and Franck-Condon approaches for calculating spectral shapes of molecules in solution
The correct treatment of vibronic effects is vital for the modeling of absorption spectra of many solvated dyes. Vibronic spectra for small dyes in solution can be easily computed within the Franck-Condon approximation using an implicit solvent model. However, implicit solvent models neglect specific solute-solvent interactions on the electronic excited state. On the other hand, a straightforward way to account for solute-solvent interactions and temperature-dependent broadening is by computing vertical excitation energies obtained from an ensemble of solute-solvent conformations. Ensemble approaches usually do not account for vibronic transitions and thus often produce spectral shapes in poor agreement with experiment. Here we address these shortcomings by combining zero-temperature vibronic fine structure with vertical excitations computed for a room-temperature ensemble of solute-solvent configurations. In this combined approach, all temperature-dependent broadening is treated classically through the sampling of configurations and quantum mechanical vibronic contributions are included as a zero-temperature correction to each vertical transition. In our calculation of the vertical excitations, significant regions of the solvent environment are treated fully quantum mechanically to account for solute-solvent polarization and charge-transfer. For the Franck-Condon calculations, a small amount of frozen explicit solvent is considered in order to capture solvent effects on the vibronic shape function. We test the proposed method by comparing calculated and experimental absorption spectra of Nile red and the green fluorescent protein chromophore in polar and non-polar solvents. For systems with strong solute-solvent interactions, the combined approach yields significant improvements over the ensemble approach. For systems with weak to moderate solute-solvent interactions, both the high-energy vibronic tail and the width of the spectra are in excellent agreement with experiments
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Mana and thermalization: Probing the feasibility of near-Clifford Hamiltonian simulation
Quantum hydrodynamics is the emergent classical dynamics governing transport of conserved quantities in generic strongly interacting quantum systems. Here, recent matrix product operator methods [1,2] have made simulations of quantum hydrodynamics in 1+1D tractable, but they do not naturally generalize to 2+1D or higher, and they offer limited guidance as to the difficulty of simulations on quantum computers. Near-Clifford simulation algorithms are not limited to one dimension, and future error-corrected quantum computers will likely be bottlenecked by non-Clifford operations. We therefore investigate the non-Clifford resource requirements for simulation of quantum hydrodynamics using mana, a resource theory of non-Clifford operations. For infinite-temperature starting states, we find that the mana of subsystems quickly approaches zero, while for starting states with energy above some threshold the mana approaches a nonzero value. Surprisingly, in each case the finite-time mana is governed by the subsystem entropy, not the thermal state mana; we argue that this is because mana is a sensitive diagnostic of finite-time deviations from canonical typicality.
1-dimensional spin chains↗
Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification
Here, we analyze the convergence of probability density functions utilizing approximate models for both forward and inverse problems. We consider the standard forward uncertainty quantification problem where an assumed probability density on parameters is propagated through the approximate model to produce a probability density, often called a push-forward probability density, on a set of quantities of interest (QoI). The inverse problem considered in this paper seeks to update an initial probability density assumed on model input parameters such that the subsequent push-forward of this updated density through the parameter-to-QoI map matches a given probability density on the QoI. We prove that the densities obtained from solving the forward and inverse problems, using approximate models, converge to the true densities as the approximate models converge to the true models. Numerical results are presented to demonstrate convergence rates of densities for sparse grid approximations of parameter-to-QoI maps and standard spatial and temporal discretizations of PDEs and ODEs.
97 MATHEMATICS AND COMPUTING↗
Implicit flux-split schemes for the Euler equations
Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.
Thomas, J. L.↗
Parametric study of grid size, time step and turbulence modeling on Navier-Stokes computations over airfoils
An upwind-biased implicit approximate factorization algorithm is applied to several steady and unsteady turbulent flows. The thin layer form of the compressible Navier-Stokes equation is used. Both the flux vector splitting and flux difference splitting methods are used to determine fluxes, and the results are compared. Flux difference splitting predicts results more accurately than flux vector splitting on a given mesh size, but, in its present implementation, is more severely limited by the maximum CFL number for unsteady time accurate flows. Physical aspects of the computations are also examined. An equilibrium turbulent boundary layer model computes generally better steady and unsteady results than a nonequilibrium model when there is little to no boundary layer separation. Conversely, when a significant region of separation exists, the nonequilibrium model performs in better agreement with experiment.
Rumsey, Christopher L.↗
Dynamical observer for a flexible beam via finite element approximations
The purpose of this view-graph presentation is a computational investigation of the closed-loop output feedback control of a Euler-Bernoulli beam based on finite element approximation. The observer is part of the classical observer plus state feedback control, but it is finite-dimensional. In the theoretical work on the subject it is assumed (and sometimes proved) that increasing the number of finite elements will improve accuracy of the control. In applications, this may be difficult to achieve because of numerical problems. The main difficulty in computing the observer and simulating its work is the presence of high frequency eigenvalues in the finite-element model and poor numerical conditioning of some of the system matrices (e.g. poor observability properties) when the dimension of the approximating system increases. This work dealt with some of these difficulties.
Manitius, Andre↗
Euler solutions to nonlinear acoustics of non-lifting hovering rotor blades
For the first time a computational fluid dynamics (CFD) method is used to calculate directly the high-speed impulsive (HSI) noise of a non-lifting hovering rotor blade out to a distance of over three rotor radii. In order to accurately propagate the acoustic wave in a stable and efficient manner, an implicit upwind-biased Euler method is solved on a grid with points clustered along the line of propagation. A detailed validation of the code is performed for a rectangular rotor blade at tip Mach numbers ranging from 0.88 to 0.92. The agreement with experiment is excellent at both the sonic cylinder and at 2.18 rotor radii. The agreement at 3.09 rotor radii is still very good, showing improvements over the results from the best previous method. Grid sensitivity studies indicate that with special attention to the location of the boundaries a grid with approximately 60,000 points is adequate. This results in a computational time of approximately 40 minutes on a Cray-XMP. The practicality of the method to calculate HSI noise is demonstrated by expanding the scope of the investigation to examine the rectangular blade as well as a highly swept and tapered blade over a tip Mach number range of 0.80 to 0.95. Comparisons with experimental data are excellent and the advantages of planform modifications are clearly evident. New insight is gained into the mechanisms of nonlinear propagation and the minimum distance at which a valid comparison of different rotors can be made: approximately two rotor radii from the center of rotation.
Baeder, J. D.↗
Euler solutions to nonlinear acoustics of non-lifting rotor blades
For the first time a computational fluid dynamics (CFD) method is used to calculate directly the high-speed impulsive (HSI) noise of a non-lifting hovering rotor blade out to a distance of over three rotor radii. In order to accurately propagate the acoustic wave in a stable and efficient manner, an implicit upwind-biased Euler method is solved on a grid with points clustered along the line of propagation. A detailed validation of the code is performed for a rectangular rotor blade at tip Mach numbers ranging from 0.88 to 0.92. The agreement with experiment is excellent at both the sonic cylinder and at 2.18 rotor radii. The agreement at 3.09 rotor radii is still very good, showing improvements over the results from the best previous method. Grid sensitivity studies indicate that with special attention to the location of the boundaries a grid with approximately 60,000 points is adequate. This results in a computational time of approximately 40 minutes on a Cray-XMP. The practicality of the method to calculate HSI noise is demonstrated by expanding the scope of the investigation to examine the rectangular blade as well as a highly swept and tapered blade over a tip Mach number range of 0.80 to 0.95. Comparisons with experimental data are excellent and the advantages of planform modifications are clearly evident. New insight is gained into the mechanisms of nonlinear propagation and the minimum distance at which a valid comparison of different rotors can be made: approximately two rotor radii from the center of rotation.
Baeder, J. D.↗